Globally stable proportional‐integral‐derivative control for spacecraft pose tracking via dual quaternions

Abstract

Due to the high reliability and simple adjustment, proportional‐integral‐derivative (PID) control is widely used in practical systems. However, intrinsic non‐linearity of the pose dynamics hinders the design of a PID pose controller. Besides, topological constraints on the rigid body configuration space SE(3) prevent a continuous or a memoryless discontinuous state feedback control from achieving robust global stability. For these two issues, this paper develops a dual quaternion‐based hybrid PID pose tracking control strategy, where the newly introduced integral term can compensate for constant disturbances, and the hysteretic switching‐based hybrid feedback can avoid both unwinding phenomenon and noise sensitivity caused by the topological constraints. In addition, by adjusting the hysteresis width, the proposed hybrid PID controller can also become a continuous or a discontinuous PID controller. The global asymptotic stability in the presence of constant disturbance forces and torques, and robustness to measurement noises are proven by the hybrid system stability theory. Numerical simulations for an earth‐orbiting spacecraft pose tracking mission are conducted to illustrate and compare the performances of the proposed hybrid, continuous and discontinuous PID pose tracking control laws.